Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
830 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19151335 | C2 | semidirect |
| 5. #26018523 | C2 | semidirect |
| 6. #26018094 | C2 | semidirect |
| 7. C2×#451×C89 | C2 | semidirect |
| 247. C2×#451 | D89 | semidirect |
| 254. C89 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151737 | 2 |
| #26026186 | 2 |
| C2×#19151335 | 2 |
| C2×#19151333 | 2 |
| #26018523 | 2 |
| #26018094 | 2 |
| C2×#451×C89 | 2 |
| #9965 | 89 |